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Recognising Algebraic Surfaces from Two Outlines

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Abstract

Photographic outlines of 3 dimensional solids are robust and rich in information useful for surface reconstruction. This paper studies algebraic surfaces viewed from 2 cameras with known intrinsic and extrinsic parameters. It has been known for some time that for a degree d=2 (quadric) algebraic surface there is a 1-parameter family of surfaces that reproduce the outlines. When the algebraic surface has degree d>2, we prove a new result: that with known camera geometry it is possible to completely reconstruct an algebraic surface from 2 outlines i.e. the coefficients of its defining polynomial can be determined in a known coordinate frame. The proof exploits the existence of frontier points, which are calculable from the outlines. Examples and experiments are presented to demonstrate the theory and possible applications.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Western Australia, Stirling Highway, Crawely, Perth, WA, 6008, Australia

    Simon Collings & Lyle Noakes

  2. School of Computer Sience and Software Engineering, University of Western Australia, Stirling Highway, Crawely, Perth, WA, 6008, Australia

    Ryszard Kozera

Authors
  1. Simon Collings
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  2. Ryszard Kozera
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  3. Lyle Noakes
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Corresponding author

Correspondence to Simon Collings.

Additional information

Simon Collings is partially funded by the Interactive Virtual Environments Centre (IVEC).

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Collings, S., Kozera, R. & Noakes, L. Recognising Algebraic Surfaces from Two Outlines. J Math Imaging Vis 30, 181–193 (2008). https://doi.org/10.1007/s10851-007-0050-5

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  • DOI: https://doi.org/10.1007/s10851-007-0050-5

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